where \(c\)  and \(H\)  are the colour metric and hard function, respectively, see
[1]}, [2]} for details of the notation. We can
write the matrix \(\mathbf {\Gamma }\)  in colour space as a sum over dipoles

B = i>jB TiTj Iij .

In our case only three dipoles, namely 12, 13 and 23, contribute to the soft function. As a consequence,
by exploiting colour conservation, all colour operators \( \mathbf {T}_i\cdot \mathbf {T}_j\)  can be written
as linear combinations of the \(SU(3)\)  Casimir invariants \(C_F\)  and \(C_A\)  and, consequently, the matrix
structure of Eq. (REF ) disappears.
The coefficients of the single-logarithmic function \(t\) , can be
obtained by integrating the matrix elements for each dipole \(ij\) 
over the appropriate phase space. Because the collinear
contributions have already been included in the radiators \(R_l\)  in
Eq. (REF ), the \(I_{ij}\)  coefficients are purely due to
soft wide-angle radiation. Consequently, they are functions of the
jet radius \(R_0\)  only, and are independent of the angularity
exponent \(\alpha \) . In particular, they coincide with those computed in [3]} for the jet mass:

I12 = R204 ,
